Integrating partial knowledge of physical principles into data-driven techniques is a primary goal of the
scientific machine learning (ML) community [1]}.
Physical principles – such as conservation laws, symmetries, and invariances – can be incorporated into ML
algorithms in the form of inductive biases, thereby ensuring that the learned models are constrained to the correct physics.
Recent successful examples of ML algorithms that have been modified to respect physical principles include
neural networks [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]},
kernel methods [11]}, [12]},
deep generative models [13]},
and sparse regression [14]}, [15]}, [16]}, [17]}, [18]}.
These examples demonstrate that incorporating partially-known physical principles into machine learning architectures
can increase the accuracy, robustness, and generalizability of the resulting models, while simultaneously
decreasing the required training data.
In this work, we integrate knowledge of physical principles into one of the most widely-used methods in data-driven dynamical systems research: the dynamic mode decomposition [19]}, [20]}, [21]}, [22]}, [23]}, [24]}.
